I am reading Harry Gensler's Introduction to Logic (Routledge, 2002) and doing exercise 1 of 7.3b in the "Basic Modal Logic" chapter. I think I follow the steps. The answer is in the book.

My question is whether this accurately reflects a pragmatist view of truth or whether a pragmatist has a way around the argument.

The exercise contains the following three lines which need to be symbolized and then tested for validity.

If the pragmatist view of truth is right, then "A is true" entails "A is useful to believe."

"A is true but not useful to believe" is consistent.

∴ The pragmatist view of truth isn't right.

One can use the following symbolization key which seems to correspond with what is in the book's answer.

P: The pragmatist view of truth is right.

B: A is useful to believe.

T: A is true.

The argument set up in this fashion can be shown to be valid even without using modal logic. I imagine a pragmatist would reject the second premise, but I don't see any obvious inconsistency.

How do pragmatists work around such an argument?

If they don't accept one or more of these premises please provide a source justifying that. If there is another modal logic that would be more appropriate for pragmatism, please provide a source for it.

Well, is caring about the true things that aren't useful, in itself useful? Then why bother to consider them true? Just mark them irrelevant and move on. If they aren't constructive or destructive, there is no benefit to assigning them a truth-value. Believing things has a cost, however minor, and believing non-useful things is therefore a waste. Besides arguing about a definition of truth with logic is like arguing about the meaning of 'and'.
– jobermarkDec 23 '18 at 19:55

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This view of truth ("truth is what works") is specific to James, and to a lesser extent Dewey, it was condemned by other pragmatists starting with Peirce, and almost all modern ones (Putnam, Habermas, etc.), see IEP. Even James and Dewey would distinguish between useful and useful-in-the-long-run, and can argue that, in the long run (spanning beyond one human life, or even that of the human race), the untrue can not be useful. According to Peirce, it is the meaning of a statement that is determined by its practical consequences, not the truth.
– ConifoldDec 24 '18 at 22:17

3 Answers
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You are making too much of old, beaten and half-dead horse. Pragmatism was an anti-philosophical movement and didn't mix well with formal logic. Main idea of pragmatism was that humanity should not waste efforts on proving or disapproving theories that don't have practical value. Main target of attack was Cartesianism and all forms of skepticism that questioned knowledge accumulated by humanity so far. Pragmatism simply stated that if theory "works" in practice, then it is useful to know it and it is true. Of course, idea that theory may "work" today (combustion engine is useful for humanity) , but it may not "work" if system changes (too much of combustion engines causes pollution and deadly diseases) did not occur to them.

As for validity of your statements, it doesn't work that way in pragmatism. Pragmatists never argued that non-useful statements must be false. Instead, they rejected binary logic of true and false, and introduced third state of "not-important" or "not useful". As mentioned before, this state was reserved for difficult and metaphysical theories and statements that made those theories, and had no practical value. Any practical statement, that could be empirically proven or disproven would not fall in this class.

+1 Would you have any sources that I could use for further information?
– Frank HubenyDec 23 '18 at 23:04

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@FrankHubeny Philosophy and the Mirror of Nature by Richard Rorty. It is relatively recent book (1979) , but it builds on foundations of earlier pragmatists, and it is anti-philosophical in a sense that it redefines the role of philosophy from establishing truth to interpreting "what works".
– rs.29Dec 24 '18 at 8:12

@FrankHubeny This post is mostly wrong. Pragmatism was not an anti-philosophical movement, many major philosophers were and are pragmatists (Rorty, Putnam, Habermas, Brandom recently). Nor did they reject classical logic, Peirce was one of the inventors of the modern predicate calculus. Pragmatism enters at the level of semantics, not logic, see e.g. Putnam and Brandom for modern treatments.
– ConifoldDec 24 '18 at 22:23

@Conifold It may be wrong, but I got the Rorty reference that I will have to check out first that is intriguing me now.
– Frank HubenyDec 24 '18 at 22:26

@FrankHubeny Rorty is an eliminativist about truth, on his view it is a confused notion best not talked about at all. Among pragmatists, he is the closest to the social constructivism and cultural relativism of postmodernists.
– ConifoldDec 24 '18 at 22:38

The true is the name of whatever proves itself to be good in the way of belief, and good, too, for definite assignable reasons. (1907)

‘The true’, to put it very briefly, is only the expedient in the way of our thinking, just as ‘the right’ is only the expedient in the way of our behaving. Expedient in almost any fashion; and expedient in the long run and on the whole, of course. (1907)

Other formulations fill this out by giving a central role to experience:

Ideas … become true just in so far as they help us to get into satisfactory relations with other parts of our experience. (1907)

Any idea upon which we can ride …; any idea that will carry us prosperously from any one part of our experience to any other part, linking things satisfactorily, working securely, saving labor; is true for just so much, true in so far forth, true instrumentally. (1907)

On this account, we may say that the second premise : "A is true but not useful to believe" must be rejected by a pragmatist.

I think you have one premise the wrong way round. It's not, for the pragmatist, that 'A is true' entails 'A is useful to believe.' Rather, 'A is useful to believe' entails 'A is true'. (Roughly, and leaving out refinements that don't appear in your question.)

'A is true but not useful to believe' is a contradiction in pragmatist terms since truth is defined in terms of usefulness.

So your 'A is true but not useful to believe' deploys a non-pragmatist theory of truth in order to refute the pragmatist theory of truth.

Therefore I don't think your premises yield a problem for pragmatism. This is not to endorse pragmatism, only to suggest that it can't be refuted via your premises.

But I think you are right to be sceptical and critical of pragmatism. References : On pragmatism and its logical problems with truth see the essay on pragmatism in Bertrand Russell's Philosophical Essays: